Phase modulated signals such as binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) may be commonly used in optical communications. Techniques to measure the complex optical field of high bit rate signals have been considered. Examples of conventional techniques for obtaining the signal trajectory and constellation diagram include linear optical sampling [1]-[3], coherent detection and post-processing of real-time sampled waveforms [4]-[7], and complex spectral analysis [8].
Previously, an interferometric approach with real-time sampling has been demonstrated for low bandwidth signals under the assumption that the relative phase between two interfering signals is stable during the measurement time (100 ns) [9]. However, techniques that rely on real-time sampling may be limited by the bandwidth and sampling rate of the oscilloscope. For example, a conventional real-time sampling oscilloscope such as a Tektronix Digital Serial Analyzer 72004B may have bandwidth and sampling rate limits of 20 GHz and 50 GSample/s, respectively.
It would be useful to allow for determination of modulated signals without such restrictions.